Question

Find the principal value of ${\cos }^{-1}\left(-\frac{1}{\sqrt{2}}\right)$

Answer 1

We have,

${\cos }^{-1}(-\frac{1}{\sqrt{2}})$

${\cos }^{-1}(-\cos \frac{\pi }{4})$

We know that

$\cos (\pi -\theta )=-\cos \theta$

Therefore,

$={\cos }^{-1}\left(\cos (\pi -\frac{\pi }{4})\right)$

$=\pi -\frac{\pi }{4}$

$=\frac{3\pi }{4}$

Hence, this is the answer.